FPT algorithms for Feedback Vertex Set parameterized by the solution size are known with running times \(\mathcal {O}^*(3.490^k)\)  (deterministic) and \(\mathcal {O}^*(2.7^k)\)  (randomized) [1]}, [2]}, [3]}.
The parameterization by treewidth has led to deterministic \(\mathcal {O}^*(11.36^k)\)  and randomized \(\mathcal {O}^*(3^k)\)  algorithms [4]}, [5]}.
Other FPT algorithms include parameterizations by deletion distance to a chordal graph, by cliquewidth and by the number of vertices of degree at least 4 [6]}, [7]}, [8]}, [9]}.
Recently, Donkers and Jansen proposed a parameterization based on the complexity of the solution structure [10]}.
They introduced the notion of antlers, similar to the notion of crown decompositions for Vertex Cover.
